A Course In Computational Number Theory - Includes Cd-Rom - Bressoud David-M

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Résumé :
This textbook is a one-semester introduction to number theory that uses the computer as a tool for motivation and explanation. The accompanying CD-ROM contains Mathematica files with all the commands and programs. The reader should be able to get on the computer quickly to begin doing personal experiments with the patterns of the integers. The presentation of the theoretical structure of number theory is integrated tightly with these explorations, arising out of them to confirm, explain, or deny what is observed experimentally, and feeding back into them to enable deeper and more sophisticated investigations. The efficiency of algorithms is always at the forefront as the book presents and explains many of the fastest algorithms for working with integers. This book covers the traditional topics, but also takes advantage of powerful software to explore factoring algorithms, primality testing, the RSA public-key cryptosystem, and unusual applications such as check digit schemes and a computation of the energy that holds a salt crystal together. Advanced topics include continued fractions, Pell's equation, and the Gaussian primes.

Biographie:
David Bressoud is DeWitt Wallace Professor and Chair of Mathematics and Computer Science at Macalester College. He was a Peace Corps Volunteer in Antigua, West Indies, and taught at Penn State before moving to Macalester in 1994, the year he won the MAA Distinguished Teaching Award. His books include Factorization and Primality Testing. Second Year Calculus: From Celestial Mechanics to Special Relativity. A Radical Approach to Real Analysis. and Proofs and Confirmations: The Story of the Alternating Sign Matrix Conjecture. STAN WAGON is Professor of Mathematics and Computer Science at Macalester College. He is a leading expert in the use of Mathematica in teaching and has written many books on that subject, such as VisualDSolve: Visualizing Differential Equations with Mathematica (with Dan Schwalbe), Animating Calculus (with Ed Packel), and the best-selling Mathematica in Action. Other books include The Banach-Tarski Paradox and the problem book, Which Way Did the Bicycle Go? (with Joseph D. E. Konhauser and Dan Velleman). In 1987, he won the Lester R. Ford Award for expository writing.

Sommaire:
["Fundamentals","Congruences, Equations, and Powers","Euler's - Function","Prime Numbers","Some Applications","Quadratic Residues","Continued Fractions","Prime Testing With Lucas Sequences","Prime Imaginaries and Imaginary Primes","Mathematica Basics","Lucas Certificates Exist."]